cdfrevgum {lmomco} | R Documentation

## Cumulative Distribution Function of the Reverse Gumbel Distribution

### Description

This function computes the cumulative probability or nonexceedance probability of the Reverse Gumbel distribution given parameters (xi and α) of the distribution computed by `parrevgum`. The cumulative distribution function of the distribution is

F(x) = 1 - e^{-e^{(-frac{(x-xi)}{α})}} mbox{,}

where F(x) is the nonexceedance probability for quantile x, xi is a location parameter, and α is a scale parameter. Notice that the function has some sign differences and uses the complement of F compared to the cumulative distribution function of the Gumbel distribution in `cdfgum`.

### Usage

    cdfrevgum(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `parrevgum` or similar.

### Value

Nonexceedance probability (F) for x.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

### See Also

`quarevgum`, `parrevgum`

### Examples

    # See p. 553 of Hosking (1995)
    # Data listed in Hosking (1995, table 29.3, p. 553)
    D <- c(-2.982, -2.849, -2.546, -2.350, -1.983, -1.492, -1.443,
           -1.394, -1.386, -1.269, -1.195, -1.174, -0.854, -0.620,
           -0.576, -0.548, -0.247, -0.195, -0.056, -0.013,  0.006,
            0.033,  0.037,  0.046,  0.084,  0.221,  0.245,  0.296)
    D <- c(D,rep(.2960001,40-28)) # 28 values, but Hosking mentions 40 values in total
    z <-  pwmRC(D,threshold=.2960001)
    str(z)
    # Hosking reports B-type L-moments for this sample are
    # lamB1 = -0.516 and lamB2 = 0.523
    btypelmoms <- pwm2lmom(z$Bbetas)
    # My version of R reports lamB1 = -0.5162 and lamB2 = 0.5218
    str(btypelmoms)
    rg.pars <- parrevgum(btypelmoms,z$zeta)
    str(rg.pars)
    # Hosking reports xi=0.1636 and alpha=0.9252 for the sample
    # My version of R reports xi = 0.1635 and alpha = 0.9254
    F  <- nonexceeds()
    PP <- pp(D) # plotting positions of the data
    D  <- sort(D)
    plot(D,PP)
    lines(D,cdfrevgum(D,rg.pars))

[Package lmomco version 0.92 Index]